The divers in order from least to greatest based on the number of liters left in their oxygen tank will be Alexis, Dante, and Sofia. The correct answer is B.
What is ascending order?In mathematics, placing numbers in ascending order refers to doing so from least to largest from left to right. When numbers are arranged in ascending order, they are done so from least to largest.
Given that three divers went scuba diving in the ocean for a couple of hours. The table for the oxygen requirement is given below:-
Diver Oxygen (liters)
Alexis Seventy nine over eighth
Dante 9.3
Sofia Nine and eight over fifteenth
The Numbers are:-
Alexis ( Seventy nine over eighth) = 79 / 9 = 8.78
Dante = 9.3
Sofia ( Nine and eight over fifteenth ) = 9(9/15} = 9.6
The arrangement from least to highest will be Alexis, Dante, and Sofia.
The correct options are given below:-
Sofia, Dante, Alexis
Alexis, Dante, and Sofia.
Dante, Alexis, Sofia
Dante, Sofia, Alexis
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Answer:
Dante, Alexis and Sofia
Step-by-step explanation:
please tell me if I'm wrong but I'm positive its Dante, Alexis and Sofia
Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
I'll assume the ODE is
[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]
Solve the homogeneous ODE,
[tex]y'' - 3y' + 2y = 0[/tex]
The characteristic equation
[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]
has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is
[tex]y = C_1 e^x + C_2 e^{2x}[/tex]
For nonhomogeneous ODE (1),
[tex]y'' - 3y' + 2y = e^x[/tex]
consider the ansatz particular solution
[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]
Substituting this into (1) gives
[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]
For the nonhomogeneous ODE (2),
[tex]y'' - 3y' + 2y = e^{2x}[/tex]
take the ansatz
[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]
Substitute (2) into the ODE to get
[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]
Lastly, for the nonhomogeneous ODE (3)
[tex]y'' - 3y' + 2y = e^{-x}[/tex]
take the ansatz
[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]
and solve for [tex]c[/tex].
[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]
Then the general solution to the ODE is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]
Solve 2tan(x)cos^2(x)=1 algebraically
No links, provide full answer
The value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
What are the family of solutions behind an equation of the form p · q = k?
In this question we have a product of two nonzero real numbers equal to 5, whose mathematical form is:
p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k
Then, we proceed to find the solutions for x and y in terms of k:
2 · x + √(4 · x² + 5) = k
2 · x = k - √(4 · x² + 5)
4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5
2 · k · √(4 · x² + 5) = k² + 5
4 · k² · (4 · x² + 5) = (k² + 5)²
4 · x² + 5 = (k² + 5)² /(4 · k²)
4 · x² = (k² + 5)² /(4 · k²) - 5
x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.
2 · y = 5 / k - √(4 · y² + 5)
4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5
(10 / k) · √(4 · y² + 5) = 25 / k² + 5
(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²
4 · y² + 5 = (k² / 100) · (25 / k² + 5)²
4 · y² = (k² / 100) · (25 / k² + 5)² - 5
y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.
Therefore, the value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
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Help me in thisssssss
Answer:
34
Step-by-step explanation:
(a + [tex]\frac{1}{a}[/tex] ) = 6← square both sides
(a + [tex]\frac{1}{a}[/tex] )² = 6² ← expand left side using FOIL
a² + 1 + 1 + [tex]\frac{1}{a^2}[/tex] = 36
a² + 2 + [tex]\frac{1}{a^2}[/tex] = 36 ( subtract 2 from both sides )
a² + [tex]\frac{1}{a^2}[/tex] = 34
What is the range of the function f(x) = |x + 4| + 2?
R: {f(x) ∈ ℝ | f(x) ≤ 2}
R: {f(x) ∈ ℝ | f(x) ≥ 2}
R: {f(x) ∈ ℝ | f(x) > 6}
R: {f(x) ∈ ℝ | f(x) < 6}
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]
You need to remember that the form of an Absolute Value Function is:
• For the vertex:
[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]
[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]
• For the definition:
If "a" is positive (+) , then the range of the function is:
[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]
If "a" is negative (-), the range of the function is:
[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]
In this case we can identify that:
[tex]\small\longrightarrow \sf{a = 1}[/tex]
[tex] \small\longrightarrow\sf{a = 2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]
Please help me solve!
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
Find the mean and standard deviation for the set of data. {16,22,8,5,20,18,14,17,24}
The mean of the set is : 16
The Slandered deviation of set : 5.8689389538863
What is mean?Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
What is Standard Deviation?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.
Calculating average:Average x = 16
Count n = 9
Sum Sum =144
Average = Sum / Count
= 144 / 9
= 16
Standard Deviation, σ: 5.8689389538863
Count, N = 9
Sum, Σx: = 144
Mean, μ: = 16
Variance, σ²: = 34.444444444444
Calculating slandered devotion:
[tex]\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}[/tex]
[tex]\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}[/tex]
[tex]=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}[/tex]
= 310/9
= 34.444444444444
σ = √34.444444444444
σ = 5.8689389538863
The mean of the set is : 16
The Standard deviation of set : 5.8689389538863
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What is the tenth term in the sequence 9, 13, 17, 21, 25…?
Step-by-step explanation:
its 29 9x4=29 9+4=13 13+4=17
Round 4709.94107458 to the nearest whole number
4710
Explanation:4709.94107458
The nearest whole number for 4709.94107458 is 4710 since the number 9 after the decimal is greater than 5. Therefore, if you add 1 to 9 before the decimal, you get 10.
Hope this helps :)
Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle?
108°
127°
150°
487°
Answer:
127
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Which graph represents the function f(x)= 2x-1 x-1 ?
Answer:
The bottom graph.
Step-by-step explanation:
The asymptote ( in between the 2 curves) on the bottom graph is at x = 1, because when x = 1 the denominator = 0.
Which graph represents (y-3)^2/25 + (x+1)^2/4 > 1 and y <= square root{x+5}+2
Answer:
B. the second graph.
Step-by-step explanation:
Literally the photo is on the question.
Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.
What is graph?The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.
Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.
Therefore, the correct option is option B.
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Point M is on line segment \overline{LN}
LN
. Given LN=2x-5,LN=2x−5, MN=x-1,MN=x−1, and LM=3,LM=3, determine the numerical length of \overline{LN}.
LN
.
Considering the relation built the presence of point M on line LN, the numerical length of LN is of 9 units.
What is the relation from the presence of point M on the line LN?Point M splits line LN into two parts, LM and MN, hence the total length is given by:
LN = LM + MN.
From the given data, we have that:
LN = 2x - 5.LM = 3.MN = x - 1.Hence we first solve for x.
LN = LM + MN.
2x - 5 = 3 + x - 1
x = 7.
Hence the total length is:
LN = 2x - 5 = 2 x 7 - 5 = 14 - 5 = 9 units.
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The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. on the bottom shelf are 3 fiction and 5 nonfiction books. choosing which 2 books describes a pair of dependent events?
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change. Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance. Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is. Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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To the nearest foot what is the length of a pendulum that makes one full swing in 1.9s
A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.
What is the length of a pendulum?A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.
Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".
Given the equation:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
where L is the length in feet and T is the time in seconds.
Given that T = 1.9sec,
Hence:
[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]
L = 2.93 feet
A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.
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cosa/2-tana +sina/1-cota=cosa+sina
Answer:
Cosa/2-tana+sina
Step-by-step explanation:
Cosatana
A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.
65% of the 800 students at North High School ride the bus. How many students ride the bus?
Answer:
800÷100 = 8
65×8=520
[tex]\frac{520}{800}[/tex]
another way:
100%-65%=35%
35% = 0.35
800×0.35= 280
800-280=520
another way:
65% = 0.65
0.65×800=520
Hope it helped! :)
Given the functions f(x) = x3 x2 – 2x 3 and g(x) = log(x) 2, what type of functions are f(x) and g(x)? justify your answer. what key feature(s) do f(x) and g(x) have in common? (consider domain, range, x-intercepts, and y-intercepts.)
The functions f(x) and g(x) are different functions
The function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common feature in both functions is their range
According to the statement
we have given that the some functions and we have to justify these functions.
The functions are given as:
f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2
This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common key features of the functions
To do this, we plot the graphs of both functions
From the attached graph, we have the following features:
Function f(x)
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y - intercept = 3
x - intercepts = -2.37
Function g(x)
Domain: x > 0
Range: -∞ < y < ∞
y - intercept = None
x - intercepts = 0.01
By comparing the key features above, we can conclude that the common features in both functions is their range.
The functions f(x) and g(x) are different functions
The function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common feature in both functions is their range
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Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions.
The roots of the given polynomials exists
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex]
What is the formula of the quadratic equation?For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Therefore by using the formula we have
[tex]$x^{2}-16 x+54=0[/tex]
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]
simplifying the equation, we get
[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]
[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]
[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]
Therefore, the roots of the given polynomials are
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex].
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67 is the difference of Gail’s height and 16.
Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of 333 for \$5$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
How do u get 3 bags of avacodes or 9 avacadoes ??
Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
EquationAmount Alonso brings to the market = $21Cost of an egg = $2.50Cost of avocados in bags of 3 = $5Number of avocados bought = x21 = 2.50 + 5x
21 - 2.50 = 5x
18.50 = 5x
x = 18.50 / 5
x = 3.7 bags of avocados
To get 3 bags of avocados or 9 avocados
= $5 × 3
= $15
Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
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Estimate the product of 0. 235 and 13. 467 to the nearest hundredth.
Answer:
3.16
Step-by-step explanation:
An estimate is usually made to 1 or 2 significant digits. Here, we want an estimate accurate to hundredths, which will be 3 significant digits.
EstimateWe can round the numbers to some reasonable values, then look at the effect of the rounding error.
0.235 × 13.467 = (0.25 -0.015) × (13.5 -0.033)
= 0.25(13.5) -0.25(0.033) -0.015(13.5) +0.015(0.033)
= 3.375 -0.00825 -0.2025 + (something small)
≈ 3.375 -0.008 -0.203 = 3.375 -0.211 = 3.164
0.235 × 13.467 ≈ 3.16
Mental mathNote that the values we have can make use of mental math methods.
0.25 = 1/4 = (1/2)(1/2)
0.015 = 0.01(1 +1/2)
That is, dividing numbers by 2 mentally is usually not terribly difficult. (Here, it is made more difficult by the odd digits involved.)
0.25 × 13.5 = (1/2)(13.5/2) = 1/2(6.75) = 3.375
0.015 × 13.5 = 0.135 +0.135/2 = 0.135 +0.0675 = 0.2025
or, recognizing that 1.35 = 1.5 -.15, ...
0.015 × 13.5 = (0.01)(1.5) × (10)(1.5-.15) = 1.5²×(.1 -.01) = .225 -.0225
__
Additional comment
A calculator gives the actual product as 3.164745, so our estimate is accurate to hundredths.
If a function has a positive average rate of change over
an interval, does that mean that the function must be increasing over that
interval? Explain.
Step-by-step explanation:
Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)
Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)
Therefore, the positive average rate of change over an interval must be increasing over that interval.
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PLEASE HELP IM STUCK
Answer:
If I'm not mistaken that is the answer
HELP ASAP!!!! PLEASEEE!!!
Answer:
2
-2
Step-by-step explanation:
Use the second equation for x = -4.
f(-4) = 2
Use the third equation for x = 3.
f(x) = -x + 1 = -3 + 1 = -2
determine the rate of change for the right side of…
Answer:
Decreasing at an increasing rate
Step-by-step explanation:
graph looks like an arch
right side is going down
right side is going down as x increases
A circle is described by the equation x2 y2 14x 2y 14 = 0. what are the coordinates for the center of the circle and the length of the radius?
Answer:
length is (-7,-1) and radius is 6
Step-by-step explanation:
We are given the expression of the equation of a circle that is
x2 + y2 + 14x + 2y + 14 = 0.
Using completing the squares:
x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.
(08.01 mc) sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. she put all the addresses in a bag and drew a random sample of 25 addresses. she then asked those families if they would volunteer to help at the shelter. she found that 18% of the families would volunteer to help at the shelter. she claims that 18% of the neighborhood families would be expected to help at the animal shelter. is this a valid inference?
Answer:
Yes, this is a valid inference because she took a random sample of the neighborhood.
Step-by-step explanation:
As we can see, Sue's survey was perfectly random and without any prejudice.
18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.
Therefore, given that she chose a representative sample of the area, her conclusion is valid.
This design is made from 1 blue circle, 4 orange circles and 16 green circles. The circles touch each othe Given that the radius of each green circle is I unit, find the exact radius of a the orange circles, b the blue circle.
The radius of the orange circle is 1.5 unit and the radius of the blue circle is 2.25 units
How to determine the radii of the circles?The figure that completes the question is added as an attachment
The orange circle
The radius of the green circle is given as:
r = 1
One and half green circle make up the radius of the orange circle.
So, the radius of the orange circle is
R = 1.5 * r
This gives
R = 1.5 * 1
R = 1.5
Hence, the radius of the orange circle is 1.5 unit
The blue circle
The radius of the orange circle is given as:
r = 1.5
One and half orange circle make up the radius of the blue circle.
So, the radius of the blue circle is
R = 1.5 * r
This gives
R = 1.5 * 1.5
R = 2.25
Hence, the radius of the blue circle is 2.25 units
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What is the end behavior of the function f(x)=12x2?
dis i know functiin of fx is ♾
Answer:
4th option
Step-by-step explanation:
the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )
f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then
• even degree and positive leading coefficient
f(x) → +∞ as x → + ∞ and
f(x) → + ∞ as x → - ∞